Algebra Examples

$- 8 i^{21} - 9 i^{42} + i^{83} + 2 i^{62}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $i^{21}$ as ${(i^{4})}^{5} i$ .

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Step 1.1.1

Factor out $i^{20}$ .

$- 8 (i^{20} i) - 9 i^{42} + i^{83} + 2 i^{62}$

Step 1.1.2

Rewrite $i^{20}$ as ${(i^{4})}^{5}$ .

$- 8 ({(i^{4})}^{5} i) - 9 i^{42} + i^{83} + 2 i^{62}$

Step 1.2

Rewrite $i^{4}$ as $1$ .

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Step 1.2.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$- 8 ({({(i^{2})}^{2})}^{5} i) - 9 i^{42} + i^{83} + 2 i^{62}$

Step 1.2.2

Rewrite $i^{2}$ as $- 1$ .

$- 8 ({({(- 1)}^{2})}^{5} i) - 9 i^{42} + i^{83} + 2 i^{62}$

Step 1.2.3

Raise $- 1$ to the power of $2$ .

$- 8 (1^{5} i) - 9 i^{42} + i^{83} + 2 i^{62}$

Step 1.3

One to any power is one.

$- 8 (1 i) - 9 i^{42} + i^{83} + 2 i^{62}$

Step 1.4

Multiply $i$ by $1$ .

$- 8 i - 9 i^{42} + i^{83} + 2 i^{62}$

Step 1.5

Rewrite $i^{42}$ as ${(i^{4})}^{10} i^{2}$ .

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Step 1.5.1

Factor out $i^{40}$ .

$- 8 i - 9 (i^{40} i^{2}) + i^{83} + 2 i^{62}$

Step 1.5.2

Rewrite $i^{40}$ as ${(i^{4})}^{10}$ .

$- 8 i - 9 ({(i^{4})}^{10} i^{2}) + i^{83} + 2 i^{62}$

Step 1.6

Rewrite $i^{4}$ as $1$ .

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Step 1.6.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$- 8 i - 9 ({({(i^{2})}^{2})}^{10} i^{2}) + i^{83} + 2 i^{62}$

Step 1.6.2

Rewrite $i^{2}$ as $- 1$ .

$- 8 i - 9 ({({(- 1)}^{2})}^{10} i^{2}) + i^{83} + 2 i^{62}$

Step 1.6.3

Raise $- 1$ to the power of $2$ .

$- 8 i - 9 (1^{10} i^{2}) + i^{83} + 2 i^{62}$

Step 1.7

One to any power is one.

$- 8 i - 9 (1 i^{2}) + i^{83} + 2 i^{62}$

Step 1.8

Multiply $i^{2}$ by $1$ .

$- 8 i - 9 i^{2} + i^{83} + 2 i^{62}$

Step 1.9

Rewrite $i^{2}$ as $- 1$ .

$- 8 i - 9 \cdot - 1 + i^{83} + 2 i^{62}$

Step 1.10

Multiply $- 9$ by $- 1$ .

$- 8 i + 9 + i^{83} + 2 i^{62}$

Step 1.11

Rewrite $i^{83}$ as ${(i^{4})}^{20} (i^{2} \cdot i)$ .

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Step 1.11.1

Factor out $i^{80}$ .

$- 8 i + 9 + i^{80} i^{3} + 2 i^{62}$

Step 1.11.2

Rewrite $i^{80}$ as ${(i^{4})}^{20}$ .

$- 8 i + 9 + {(i^{4})}^{20} i^{3} + 2 i^{62}$

Step 1.11.3

Factor out $i^{2}$ .

$- 8 i + 9 + {(i^{4})}^{20} (i^{2} \cdot i) + 2 i^{62}$

Step 1.12

Rewrite $i^{4}$ as $1$ .

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Step 1.12.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$- 8 i + 9 + {({(i^{2})}^{2})}^{20} (i^{2} \cdot i) + 2 i^{62}$

Step 1.12.2

Rewrite $i^{2}$ as $- 1$ .

$- 8 i + 9 + {({(- 1)}^{2})}^{20} (i^{2} \cdot i) + 2 i^{62}$

Step 1.12.3

Raise $- 1$ to the power of $2$ .

$- 8 i + 9 + 1^{20} (i^{2} \cdot i) + 2 i^{62}$

Step 1.13

One to any power is one.

$- 8 i + 9 + 1 (i^{2} \cdot i) + 2 i^{62}$

Step 1.14

Multiply $i^{2} \cdot i$ by $1$ .

$- 8 i + 9 + i^{2} \cdot i + 2 i^{62}$

Step 1.15

Rewrite $i^{2}$ as $- 1$ .

$- 8 i + 9 - 1 \cdot i + 2 i^{62}$

Step 1.16

Rewrite $- 1 i$ as $- i$ .

$- 8 i + 9 - i + 2 i^{62}$

Step 1.17

Rewrite $i^{62}$ as ${(i^{4})}^{15} i^{2}$ .

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Step 1.17.1

Factor out $i^{60}$ .

$- 8 i + 9 - i + 2 (i^{60} i^{2})$

Step 1.17.2

Rewrite $i^{60}$ as ${(i^{4})}^{15}$ .

$- 8 i + 9 - i + 2 ({(i^{4})}^{15} i^{2})$

Step 1.18

Rewrite $i^{4}$ as $1$ .

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Step 1.18.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$- 8 i + 9 - i + 2 ({({(i^{2})}^{2})}^{15} i^{2})$

Step 1.18.2

Rewrite $i^{2}$ as $- 1$ .

$- 8 i + 9 - i + 2 ({({(- 1)}^{2})}^{15} i^{2})$

Step 1.18.3

Raise $- 1$ to the power of $2$ .

$- 8 i + 9 - i + 2 (1^{15} i^{2})$

Step 1.19

One to any power is one.

$- 8 i + 9 - i + 2 (1 i^{2})$

Step 1.20

Multiply $i^{2}$ by $1$ .

$- 8 i + 9 - i + 2 i^{2}$

Step 1.21

Rewrite $i^{2}$ as $- 1$ .

$- 8 i + 9 - i + 2 \cdot - 1$

Step 1.22

Multiply $2$ by $- 1$ .

$- 8 i + 9 - i - 2$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $i$ from $- 8 i$ .

$9 - 9 i - 2$

Step 2.2

Subtract $2$ from $9$ .

$7 - 9 i$